Complex Numbers (id: e81278f9e)

本题目来源于试卷: Complex Numbers，类别为 IB数学

[问答题]
Consider the complex numbxichpb pf z:hw*q*5. 5yi,,gb ers d6)n li,ei653dmp ecff3f5qo $z_1=3\mathrm{cis}\left({120}^{\circ }\right)$ and $z_2=2+2\mathrm{i}$ .
1. Calculate $\frac{z_1}{z_2}$ giving your answer both in modulus-argument form and Cartesian form.
2. Use your results from part (a) to find the exact value of $\sin {15}^{\circ }\cdot \sin {45}^{\circ }\cdot \sin {75}^{\circ }$ , giving your answer in the form $\frac{\sqrt{a}}{b}wherea,b\in {\mathbb{Z}}^{+}$ .

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